In an interview with 680-AM radio in Atlanta, Wren said the Braves put parameters on the deal that expired Tuesday.

How unlikely is it that Dempster could still wind up in Atlanta?

"I'm not going to paint us in a corner one way or another,'' Wren said. "Let's just say that we have moved on. And we’re looking for impact pitching, someone that can make a difference for us as we go down the stretch the last two months. We feel we can win our division. But we feel we need to improve our starting pitching.''

Numerous media outlets reported Monday that a deal to bring Dempster to the Braves had been agreed to. But Dempster, as a player with 10 years of major-league service, the last five with the same team, has the right to block any trade.

Dempster is still very much in the mix for the Los Angeles Dodgers, major league sources told FOX Sports' Ken Rosenthal. The Dodgers were still negotiating with the Cubs as of Tuesday night.

As for the Braves' next move?

"These things don't move in the time frame that you want them to move, whether Ryan Dempster was our top choice, or others,'' Wren told 680-AM. "We don't have control of when the other team's ready to make a deal. We've had guys that we like a lot and we think they're difference makers and there's still some of those pitchers out there, and we’ll see how it goes.''

Dempster is eligible for free agency at the end of the season. The Cubs, under the new collective-bargaining agreement, would receive a draft pick for him only if they made him a one-year offer in the $12 million range.

If Dempster approves a trade, he might only be with his new team only for a short period of time. But he still would prefer to be on the west coast, one source said.

Dempster, a native of Gibsons, British Columbia, still has family in the Vancouver area. He has three children – Brady, 5; Riley, 3; and Finlay, 1 – and wants them to be close to his relatives, sources said.

Riley suffers from DiGeorge Syndrome, a genetic disorder that makes it difficult to swallow and eat and can create numerous other symptoms. She underwent surgeries to insert a tracheal tube and feeding tube when she was a baby.